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Question: this homework set pertains to the prediction or the analysis...

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This homework set pertains to the prediction (or the analysis) of the performance of an aircraft before (or after) a failure has occurred during a maneuver. The question is whether undergraduate mathematics can predict the result. The translation of the following information some of which may be superfluous-into mathematical formulae constitutes a part of the homework On 24 June 1994 at Fairchild Air Force Base, for some time t <0, a 185,000-pound B-52H aireraft [2] had been flying along a horizontal path, with zero vertical velocity, a forward horizontal velocity below 170 knots (nautical miles per hour) and at a constant altitude for which estimates vary between 150 and 200 feet above the ground with an angle of bank about 45deg [12, p. 277-2781. See also [7, p. 31, [16, Appendix 3, Case #12, p. 3.20). At time t 0, the aircraft rolled into a banking angle 90° (between the horizontal and the wings), which directed all the lift generated by the wings horizontally, then to 95 at 150 knots. In other words, at time 0, the vertical lift became zero, and the aircraft began a vertical free fall sideways (with both wings aligned in a vertical plane). The wingspan is 18 feet [2]. Therefore, fort20, the only vertical forces acting on the aircraft were the Earths gravity, which causes arn acceleration of about 32.174 feet per second per second downward, and vertical air resistance, which causes a drag force, Fo. hence an acceleration in the direction opposite to the vertical velocity, depending on the Reynolds number, where u [m/s] is the velocity and d [m] is some measure of length or size of the aircraft, and ρ 1.225 [kg/m) and μ ~ 0.19/104 [kg/m s] are the density and viscosity of air, so that v 1.9/105 [m2/s] [ 10, p. 129 & Table 3, p. 130] Information on the lateral drag of an aircraft seems not available, but some information is. If R>1, then the force Fo is proportional to o2 and a constant CD [10, p. 130-131].[17, p. 2) A is the area of the projection of the aircraft on a plane perpendicular to the velocity v. [3. p. 4. 16). 19 For a sphere of radius r or diameter d 2r moving in any direction, so that the projected area is A-/4, if 103<R<10, then CD0.47 for a sphere and Co1 for a cylinder, while if 3-10s < R, then CD0.20 for a sphere and CO ~ 0.4 for a cylinder, [17, Figure i I.Ii0. p. i 31, Figure il, If R < 1, then the drag force on the sphere is [10, p. 130] R<1 840 For a cylinder of diameter d and length & moving in a direction perpendicular to its axis, so that the projected area is A-d l, if R< 0.3, then the drag force is1]. [5). [8, Eq. (4.1), p 40]. (17, p. 6 & Fig. 11. D. R < 0.3 2-In () where γ is Eulers constant, γ limn-oo [(Σ.1 )-In(n)] [15.11.3. Exercise 44, p. 7671 Aircrafts reaction time may be 3 seconds to stop a roll with a maximum rate 30deg[ p. AA-2.11 & AA-2.15], several forces (accelerations) is their sum. Also, a force is the product of a mass and an acceleration: -m.a Pilots reaction time to foreseen events is about one second [131, but in emergencies six [14] to twelve [4] seconds. For this mathematical homework, take for granted from physics that the force (and acceleration) resulting from Problem 1 Determine the duration of the aircrafts fall: Calculate the time when the aircraft hits the ground. (1.1) First, neglect the air resistance; denote the falls duration by ty. Include the wingspan [11, p. AA-2.13] (1.2) Second, include the air resistance; denote the falls duration by tz. Include the wingspan. Find t (1.3) Is there sufficient time to roll back to a horizontal flight, to get back to a banking angle odeg? (1.4) Is there sufficient time to eject [11, p. AA-2.5]? You may use any information available, above, in the reference, or anywhere else, but credit sources.
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